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Robust Estimation In Heteroscedastic Linear Models
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Book Synopsis Robust Estimation in Heteroscedastic Linear Models by : Raymond J. Carroll
Download or read book Robust Estimation in Heteroscedastic Linear Models written by Raymond J. Carroll and published by . This book was released on 1981 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a heteroscedastic linear model in which the variances are a parametric function of the mean responses and a parameter theta. We propose robust estimates for the regression parameter beta and show that, as long as a reasonable starting estimate of theta is available, our estimates of beta are asymptotically equivalent to the natural estimate obtained with known variances. A particular method for estimating theta is proposed and shown by Monte-Carlo to work quite well, especially in power and exponential models for the variances. We also briefly discuss a 'feedback' estimate of beta. (Author).
Book Synopsis Robust Estimation in the Heteroscedastic Linear Model When There are Many Parameters by : Raymond J. Carroll
Download or read book Robust Estimation in the Heteroscedastic Linear Model When There are Many Parameters written by Raymond J. Carroll and published by . This book was released on 1980 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study estimation of regression parameters in heteroscedastic linear models when the number of parameters is large. The results generalize work of Huber (1973), Yohai and Maronna (1979), and Ruppert and Carroll (1989). (Author).
Book Synopsis Robust Estimation with Discrete Explanatory Variables by : Pavel Cizek
Download or read book Robust Estimation with Discrete Explanatory Variables written by Pavel Cizek and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The least squares estimator is probably the most frequently used estimation method in regression analysis. Unfortunately, it is also quite sensitive to data contamination and model misspecification. Although there are several robust estimators designed for parametric regression models that can be used in place of least squares, these robust estimators cannot be easily applied to models containing binary and categorical explanatory variables. Therefore, I design a robust estimator that can be used for any linear regression model no matter what kind of explanatory variables the model contains. Additionally, I propose an adaptive procedure that maximizes the efficiency of the proposed estimator for a given data set while preserving its robustness.
Book Synopsis Introduction to Robust Estimation and Hypothesis Testing by : Rand R. Wilcox
Download or read book Introduction to Robust Estimation and Hypothesis Testing written by Rand R. Wilcox and published by Academic Press. This book was released on 2012-01-12 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book focuses on the practical aspects of modern and robust statistical methods. The increased accuracy and power of modern methods, versus conventional approaches to the analysis of variance (ANOVA) and regression, is remarkable. Through a combination of theoretical developments, improved and more flexible statistical methods, and the power of the computer, it is now possible to address problems with standard methods that seemed insurmountable only a few years ago"--
Book Synopsis Heteroscedastic Linear Model Estimation Based on Ranks by : Themba Louis Nyirenda
Download or read book Heteroscedastic Linear Model Estimation Based on Ranks written by Themba Louis Nyirenda and published by . This book was released on 2009 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: For standard estimators, data that are heteroscedastic in nature contain outlying values which can lead to poor performance. In this study, we present a robust interactive method for estimating the location and scale parameters in the general linear model, using a rank based method. It is assumed that the errors are symmetric about 0 and the variance function model is nonlinear with respect to the scale coefficients and the design. The function is known up to a scale constant. We propose taking the logarithm of the absolute values of the variance function to linearize it. The rank estimation of the scale coefficients amounts to regressing logs of absolute residuals from an initial rank based fit on to the design. The resulting scale coefficient estimates are used to form scale constants in a weighted signed-rank method. Thus, iterating between these two rank based methods leads to the desired estimates that are obtained from linear model fits for both types of coefficients. For the heteroscedastic linear model under consideration, this study has made the following contributions: (1) the asymptotic normality results that are established here show that the estimators are both consistent and highly efficient; (2) in each estimation problem, the Iterated Reweighted Least Squares (IRWLS) formulation for rank methods of Sievers and Abebe (2004) is employed with the other parameter substituted by their corresponding estimates from an appropriate iteration; (3) the high efficiency and good robustness qualities of the proposed method are confirmed by simulation trials that were conducted in two-sample problem, several groups and general linear models; (4) the inlier issue that is a consequence of employing the log transformation is also investigated and shown to be well curtailed by the proposed method and (5) finally, the method is shown to outperform other methods when applied to real life data from a Psychiatric Clinical Trial containing two treatments, one covariate, and one confounding variable. Thus, for samples larger than 20, the proposed method is highly robust and efficient under non-normal distributions.
Book Synopsis On Efficient and Robust Estimation in Semiparametric Linear Regression Models with Missing Data by : Alex Catane Bajamonde
Download or read book On Efficient and Robust Estimation in Semiparametric Linear Regression Models with Missing Data written by Alex Catane Bajamonde and published by . This book was released on 1991 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Robust Nonlinear Regression by : Hossein Riazoshams
Download or read book Robust Nonlinear Regression written by Hossein Riazoshams and published by John Wiley & Sons. This book was released on 2018-06-11 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to discuss robust aspects of nonlinear regression—with applications using R software Robust Nonlinear Regression: with Applications using R covers a variety of theories and applications of nonlinear robust regression. It discusses both parts of the classic and robust aspects of nonlinear regression and focuses on outlier effects. It develops new methods in robust nonlinear regression and implements a set of objects and functions in S-language under SPLUS and R software. The software covers a wide range of robust nonlinear fitting and inferences, and is designed to provide facilities for computer users to define their own nonlinear models as an object, and fit models using classic and robust methods as well as detect outliers. The implemented objects and functions can be applied by practitioners as well as researchers. The book offers comprehensive coverage of the subject in 9 chapters: Theories of Nonlinear Regression and Inference; Introduction to R; Optimization; Theories of Robust Nonlinear Methods; Robust and Classical Nonlinear Regression with Autocorrelated and Heteroscedastic errors; Outlier Detection; R Packages in Nonlinear Regression; A New R Package in Robust Nonlinear Regression; and Object Sets. The first comprehensive coverage of this field covers a variety of both theoretical and applied topics surrounding robust nonlinear regression Addresses some commonly mishandled aspects of modeling R packages for both classical and robust nonlinear regression are presented in detail in the book and on an accompanying website Robust Nonlinear Regression: with Applications using R is an ideal text for statisticians, biostatisticians, and statistical consultants, as well as advanced level students of statistics.
Book Synopsis Robust Estimation of Linear Aspects in Average Contaminated Linear Models by : Viktor Kurotschka
Download or read book Robust Estimation of Linear Aspects in Average Contaminated Linear Models written by Viktor Kurotschka and published by . This book was released on 1988 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Robust Estimation and Hypothesis Testing by : Rand R. Wilcox
Download or read book Introduction to Robust Estimation and Hypothesis Testing written by Rand R. Wilcox and published by Elsevier. This book was released on 2005-01-22 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised book provides a thorough explanation of the foundation of robust methods, incorporating the latest updates on R and S-Plus, robust ANOVA (Analysis of Variance) and regression. It guides advanced students and other professionals through the basic strategies used for developing practical solutions to problems, and provides a brief background on the foundations of modern methods, placing the new methods in historical context. Author Rand Wilcox includes chapter exercises and many real-world examples that illustrate how various methods perform in different situations. Introduction to Robust Estimation and Hypothesis Testing, Second Edition, focuses on the practical applications of modern, robust methods which can greatly enhance our chances of detecting true differences among groups and true associations among variables. * Covers latest developments in robust regression * Covers latest improvements in ANOVA * Includes newest rank-based methods * Describes and illustrated easy to use software
Book Synopsis Robust Estimation Based on Grouped-adjusted Data in Linear Regression Models by : Stanford University. Econometric Workshop
Download or read book Robust Estimation Based on Grouped-adjusted Data in Linear Regression Models written by Stanford University. Econometric Workshop and published by . This book was released on 1985 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Models written by Heng Keong Leong and published by . This book was released on 1989 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Robust Estimation in Structured Linear Regression by : Lamine Mili
Download or read book Robust Estimation in Structured Linear Regression written by Lamine Mili and published by . This book was released on 1993 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Robust Estimation and Inference for Generalized Linear Models by : Eva Cantoni
Download or read book Robust Estimation and Inference for Generalized Linear Models written by Eva Cantoni and published by . This book was released on 1999 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Parameter Estimation and Hypothesis Testing in Linear Models by : Karl-Rudolf Koch
Download or read book Parameter Estimation and Hypothesis Testing in Linear Models written by Karl-Rudolf Koch and published by Springer. This book was released on 2012-12-22 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: A treatment of estimating unknown parameters, testing hypotheses and estimating confidence intervals in linear models. Readers will find here presentations of the Gauss-Markoff model, the analysis of variance, the multivariate model, the model with unknown variance and covariance components and the regression model as well as the mixed model for estimating random parameters. A chapter on the robust estimation of parameters and several examples have been added to this second edition. The necessary theorems of vector and matrix algebra and the probability distributions of test statistics are derived so as to make this book self-contained. Geodesy students as well as those in the natural sciences and engineering will find the emphasis on the geodetic application of statistical models extremely useful.
Book Synopsis Estimation of Linear Models Under Heteroscedasticity by : R. V. S. Prasad
Download or read book Estimation of Linear Models Under Heteroscedasticity written by R. V. S. Prasad and published by LAP Lambert Academic Publishing. This book was released on 2014-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the Present book Chapter I is an introductory one. It contains the general introduction about the problem of heteroscedasticity. Chapter II describes some aspects of linear models with their inferential problems. It deals with some basic statistical results about Gauss-Markov linear model besides the restricted least squares estimation and its application to the tests of general linear hypotheses. Chapter III presents a brief review on the existing estimation methods for linear models under the various specifications of heteroscedastic variances. Chapter IV deals with the analysis and examination of different types of residuals with their applications in the regression analysis. It also contains the restricted residuals in 'Seemingly Unrelated Regression' (SUR) systems. Chapter V proposes some new estimation procedures for linear models under heteroscedasticity. Chapter VI depicts the conclusions .Several references articles regarding the estimation for linear models under heteroscedasticity have been presented under a title "BIBLIOGRAPHY."
Book Synopsis Robust Estimation and Inference for Generalized Linear Models by : Eva Cantoni
Download or read book Robust Estimation and Inference for Generalized Linear Models written by Eva Cantoni and published by . This book was released on 1999 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Robust Estimation in Linear Model With Many Instruments by : Mikkel Soelvsten
Download or read book Robust Estimation in Linear Model With Many Instruments written by Mikkel Soelvsten and published by . This book was released on 2005 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first chapter of this dissertation considers a new class of robust estimators in a linear instrumental variables (IV) model with many instruments. The estimators are generalized method of moments (GMM) estimators, and the class includes the limited maximum likelihood estimator (LIML) as a special case. Each estimator in the class is consistent and asymptotically normal under many instruments asymptotics, and this chapter provides consistent variance estimators that are of the ``sandwich'' type and can be used to conduct asymptotically correct inference. Furthermore, this chapter characterizes an optimal robust estimator among the members of the class. Compared to LIML, the optimal robust estimator is less influenced by outliers and more efficient under thick-tailed error distributions. In an empirical example (Angrist and Krueger, 1991), the optimal robust estimator is approximately 80 percent more efficient than LIML. The second chapter of this dissertation provides a central limit theorem based on Stein's method (Stein, 1972) which is an integral component in the proof of the main theorem in the first chapter. It also appears to be general enough in its scope that it can be applied to a variety of other problems.
